Carlos Brathwaite and Denesh Ramdin steered West Indies into the World Twenty20 semi-finals with one Group One game to spare after a dramatic three-wicket victory over South Africa in Nagpur.

With nine runs needed from the final over to complete a chase of 123, Brathwaite took his side to the brink by crashing Kagiso Rabada’s second ball for six before Ramdin finished the job with a cut that was dropped at short third man by Hashim Amla.

The nervy finish never looked likely when West Indies ended the 13th over on 84 for three with Marlon Samuels and Dwayne Bravo at the crease. But after Bravo departed Imran Tahir struck twice in successive balls in the 17th over and Samuels lost his head in the penultimate over to leave 10 runs needed from seven balls.

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Brathwaite and Ramdin then ensured West Indies claimed their third consecutive victory, a result which means England will join them in the last four if they beat Sri Lanka.

Chris Gayle was fit enough to bat after a hamstring niggle but could not produce the heroics that overwhelmed England in their first match and was bowled by a late Rabada inswinger for four. Andre Fletcher also went in a powerplay that ended on 37 for two, run out by a brilliant direct hit from Rilee Rossouw at point, but Johnson Charles and Samuels added 32.

Charles holed out for 32 off David Wiese and, after Samuels and Bravo both passed 1,000 Twenty20 international runs, the latter slapped Aaron Phangiso to backward point with 36 required from the same number of balls.

Tahir then dragged South Africa back into the game when Andre Russell was caught at deep midwicket and Darren Sammy was bowled by a wrong ’un. Samuels sliced Chris Morris down to the third-man rope twice in the penultimate over but then recklessly picked out long-on, leaving Brathwaite and Ramdin to finish the job.

Earlier West Indies had bowled brilliantly to restrict South Africa to 122 for eight after Sammy won the toss, Russell, Bravo and Gayle each taking two economical wickets.

Quinton de Kock held the innings together with 47 from 46 balls and was well supported by lower-order contributions from Wiese (28) and Morris (16 not out) to get the Proteas to a competitive total.

An unbroken stand between Steve Smith and Shane Watson helped knock Pakistan out of the tournament as Australia kept their hopes alive with a 21-run victory in Mohali.

Smith hit 61 from 43 balls and Watson 44 from only 21 deliveries as Australia reached 193 for four. Pakistan made a decent fist of their chase but, with the required rate climbing, James Faulkner took five for 27 as Pakistan finished on 172 for eight.

Having already lost to the Group Two leaders, New Zealand, and India, Pakistan’s third defeat of the tournament means they go out. Australia face India on Sunday and the winner will join New Zealand in the semi-finals.

“Steve batted exceptionally well today but I am not surprised,” Faulkner said. “I have seen him play T20 over here in the IPL and he does that all the time. He was a class act. After losing the first two wickets it was beautiful timing to get a bit of a platform.”